Mathematics

Problem

Triangle

ABC

is constructed with

AB = 6\text{ cm}

AC = 5\text{ cm}

and

\angle A = 50^{\circ}

. Keeping

AB

fixed, the vertex

C

is erased. What is the locus of all possible positions of a new point

X

such that

\triangle ABX

is congruent to the original

\triangle ABC

? a) All points on a circle of radius

5\text{ cm}

centred at

A

b) Exactly one point c) Exactly two points d) All points on both circles of radius

5\text{ cm}

centred at

A

and

B